Level-Set Methods for Finite-Sum Constrained Convex Optimization
Authors: Qihang Lin, Runchao Ma, Tianbao Yang
ICML 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we evaluate the numerical performance of the proposed methods on Neyman-Pearson classification problem (Tong et al., 2016) formulated as in (4), where we choose φ to be the smoothed hinge loss function, i.e., a function φ(z) that equals 1/2 z, if z 0, 1/2(1 z)2 if 0 < z 1, and 0 if z > 1. We will compared the IN-LS method and our AM-FLS method using Algorithm 5 and the deterministic Mirror-Prox method (Nemirovski, 2004) to solve (6) as oracles. The comparison also involve the stochastic gradient methods by Lan & Zhou (2016) and Yu et al. (2017). The dataset we use is the rcv1 training data set from LIBSVM library 5. |
| Researcher Affiliation | Academia | 1Management Sciences Department, University of Iowa, Iowa City, IA, USA 2Computer Science Department, University of Iowa, Iowa City, IA, USA. |
| Pseudocode | Yes | Algorithm 1 IN-LS Method (Aravkin et al., 2016); Algorithm 2 AM-FLS Method; Algorithm 3 Check Gap(x, w, ε, θ); Algorithm 4 SVRG( x(0), w(0), µ, ν, ζ, ε, θ) for (9); Algorithm 5 (U(r), L(r), S(r), x) = A(r, ε, θ) |
| Open Source Code | No | The paper mentions external libraries like LIBSVM and provides links to datasets, but it does not provide any explicit statement or link to the authors' own source code for the methodology described in the paper. |
| Open Datasets | Yes | The dataset we use is the rcv1 training data set from LIBSVM library 5. It has n = 20, 242 data points with a dimension of d = 47, 236, among which the n0 = 10, 491 positive data points are used in the objective function and n1 = 9, 751 negative data points are used in the constraint of (4). 5www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/binary.html |
| Dataset Splits | No | The paper describes the partitioning of data into positive and negative sets for the problem formulation but does not provide specific training/validation/test dataset splits (e.g., percentages, sample counts, or predefined splits) for typical machine learning evaluation reproducibility. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions using the 'LIBSVM library' and implementing in 'Python', but it does not specify version numbers for these or any other software components, making the software environment not fully reproducible. |
| Experiment Setup | Yes | We choose λ = 5 and r1 = 0.1 in (4). The inner loop of SVRG is terminated after passing the data set twice. We choose τ and σ to be 10 and ζ0 = 10^-3 in SVRG instead of the theoretical values for a good practical performance. ... All the stochastic methods in the comparisons are implemented using mini-batch to construct the (standard or variance-reduce) stochastic gradients with a batch size of 5000. |